Track Geometry NMRA Cleveland Convention July 16, 2014

Andy Blenko Good track work is the most essential component of good operations

Track Spacing – Straight Track

. Mainline – 1-13/16” min. per NMRA Sheet S-8 (HO Scale); 2-1/16” preferred . Curves – depends on the radius & length of equipment Track Spacing – Straight Track •Yards – 2 inch minimum; I went with 2-1/2 inch •Staging – add width for limited access Curved Track Radii Different Equipment has Different Requirements*

* Many manufacturers recommend 24-inch minimum radius for larger locomotives and rolling stock. Curved Track Radii Good Operations vs. Good Appearance Curved Track Radii Mixed Car Lengths Present Problems with Tighter Turns Curved Track Radii • Select the largest radius turn you can live with. • Assure adequate spacing between tracks for the type/length of equipment you plan to operate.

* Photos above show 27”, 29-1/2” and 32” radius curves on 2-1/2” C-C spacing. Laying Out Curves

. Ribbonrail alignment gauges will help you lay the track to a desired radius, but won’t help you lay out the curve on your sub- roadbed. Laying Out Curves

. A trammel made from a yard stick is a tried and true method of drawing a curve of a desired radius but, you must have enough room to place the pivot point at the center of the circle. Laying Out Curves

. R Laying Out Curves

PI – Point of Intersection PC – Point of Curvature PT – Point of Tangency RP – Radius Point Δ – Delta, or Central Angle Laying Out Curves Degree of Curvature

A n-degree curve turns n degrees in the forward direction over 100 feet of chord length. (use 100 foot chord at your modeling scale) Degree of Curvature – the higher the degree of curvature, the smaller the radius and the sharper the turn. Laying Out Curves Turnouts . Turnout radius should be consistent with curve radius Reverse Curves Reverse Curves . Problem is magnified with longer car lengths . A segment of straight track is needed between curves (one car length min.) Grades

. Grade percentage is simply rise divided by run times 100

Example: If track climbs 1 inch in 8 feet (96 inches), the slope is (1/96) = 0.0104 x 100 = 1.04%

1 inch 8 feet (96 inches) Setting Grades

. Problematic to rely on a bubble level . Basement floors are anything but level . Drop ceilings are typically set with a laser level, and so can be used for reference . A surveyor’s level and rod (or yardstick) are most accurate of all Setting Grades Grades on Curves

. Grades will differ on parallel curved tracks; tighter radius curves will have a steeper grade

Reason: Even though the vertical climb (or fall) is the same, the length traveled is less on inside turns. Grades on Curves

Example: Three parallel tracks in a helix having radii of 27”, 29-1/2” and 32”. All tracks rise 4 inches in a full revolution.

Curve Radius Rise Distance per Slope Revolution 27” 4” 169.6” 2.36% 29-1/2” 4” 185.3” 2.16% 32” 4” 201.1” 1.98% Vertical Clearances . Consider roadbed thickness and max. height of equipment when planning for clearances Vertical Clearances

. NMRA Track Gauge comes from AAR “Plate C – Equipment Diagram for Limited Interchange Service” Up ‘n Over Vertical Clearance

. Circumference = 2 x 3.1416 x radius . Smaller Radius = Steeper Grade Effect of Grades

. Both grades and curves create resistance which must be overcome by your motive power. . Combining a curve on a grade will give the effect of a steeper grade due to the additional resistance of the curve. . A degree of curve is equal to a resistance of a 0.04% grade. . Prototype railroads reduce grades in curves to compensate for this additional resistance. Effect of Grades

An Example to Illustrate: A railroad has a 1.25% ruling grade, but with a curve of 25 degrees (32-inch radius in HO scale) near the summit. The effect of the curve resistance can be eliminated by reducing the grade through the curve by 0.04 x 25, or 1.0%. Reducing the grade through the curve by 1.0% , the actual grade through the curve is now 0.25%, while the effective grade will remain at 1.25% for the entire ascent. Vertical Curves . Consider using a vertical curve to ease the transition . Vertical Clearances may be critical entering or leaving a sloped track section Spiral Transition

TS TS

Easements Into Curves (also called Spirals) Easements Into Curves (also called Spirals) Easements Into Curves (also called Spirals) Easements Into Curves (see handout)

•Transition from straight track to curved track •Length of easement = longest car or loco Spiral Templates from October 1969 MR Article by Bruce Bardes The “bent stick” method will give you satisfactory results Superelevation Superelevation

. The practice of elevating the rail on the outside of a curve to help counteract the outward centrifugal forces . The “equilibrium speed” exactly balances the train through the curve . Prototype railroads elevate the outside rail no more than 5-6 inches Superelevation

. Too much superelevation can tip over a stopped train . In practice, it is difficult to set the degree of superelevation due to varying train speeds . Superelevation should transition through the curve easement Keep it Interesting!

. There is likely a prototype somewhere out there for almost anything you’d like to put on your layout! . Industrial tracks offer great opportunities to do interesting track plans in tight spaces.

Final Thoughts

. Recommend John Armstrong’s Track Planning for Realistic Operation . Test run track extensively before building scenery . Don’t be afraid to tear up and relay track for corrections; you’ll be glad you did The End

Andy & Charlie Blenko, Pittsburgh Mainline http://pittsburghmainline.weebly.com Parts of a Simple Curve

A simple curve is a circular arc joining two tangents.

As the tangent lines are extended, they meet at a point of intersection (PI) or vertex (V)

Where the arc meets the tangent, it is called the point of curvature (PC) or the point of tangency (PT)

Radial lines, perpendicular to the tangent lines, extended from the PC and PT meet at the radius point (RP)

The deflection angle (Δ) formed by the tangent lines is equal to the central angle or delta (Δ) formed by the radial lines. Calculator examples use decimal degrees.

The tangent distance (T) is the distance from the PC to the PI or the distance from the PI to the PT, both tangents are equal, where

T = R tan ( ½ Δ )

to calculate the tangent distance from the radius and delta (decimal degrees): Δ / 2 t * R =

to calculate the radius: from the tangent and delta (decimal degrees): Δ / 2 t r * T =

The long chord (LC) is the straight line distance from the PC to the PT, where

LC = 2 R sin (½ Δ )

to calculate the long chord from the radius and delta (decimal degrees): Δ / 2 s * R * 2 =

The external (E) is the distance from the PI to the midpoint of the curve, where

E = R ( ( 1/cos ( ½ Δ ) ) – 1 )

to calculate the external from the radius and delta (decimal degrees): Δ / 2 = c r - 1 = * R =

to calculate the radius from the external and delta (decimal degrees): Δ / 2 = c r - 1 = r * E =

Degree of Curve and Chords

The definition of degree of curve (D), for railroads, is the deflection angle or central angle used for a 100 ft. chord curve (in scale feet).

Let SC be a scaled 100 ft. chord, so in HO scale; SC = 100/87 * 12 or SC = 13.8 inches.

R = 50 / sin ( ½ D )

or

scaled R = ( SC / 2 ) / sin ( ½ D ) so a 18 curve has a radius of 5729.65 feet, or 790 inch radius for HO, and a 58 curve has a radius of 1146.28 feet, or 158 inch radius for HO.

D = 2 * arcsin ( 50 / R )

or

D = 2 * arcsin ( ( SC / 2 ) / scaled R )

to calculate the degree of curve for a given scaled radius in inches: SC / 2 / scaled R = S * 2 = (some calculators will have different keys for the arcsin function) so a 24” radius in HO is a 33.48 curve.

To draw points for a 24” radius, at the PC, turn a half deflection angle of 16.78 and extend it 13.8”, then, off of that chord, turn a full deflection angle of 33.48 and extend it 13.8”.

Now to draw points more frequently, we’ll use a given chord (C)

Δ = 2 * arcsin ( ( C / 2 ) / scaled R )

to calculate the deflection angle for a 24” radius using 4” chords: C / 2 / R = S * 2 =

To draw points for a 24” radius, at the PC, turn a half deflection angle of 4.88 and extend it 4”, then, off of that chord, turn a full deflection angle of 9.68 and extend it 4”, repeat the full deflection chords as needed through the curve.

O" 1" 2" 3" 4" 5" 6" 7" 8" 9" 1O" 11" 12" 13" 14" 15" 16" 17" 18" 19" 2O" 21" 22" 23" 24" 25" Tangent extension line

72" 64" radius radius 60" TS radius TX 0" TEMPLATE A For approach to curves

48" radius from 24" to 72" radius

Circle finder 42" radius

72" to center 64" to center points P 60" to center 48" to center

42" to center 1" 36" to center

34" to center 36" radius SC locations 32" to center

30" to center for various radii

34" radius 28" to center 26" to center

32" radius 24" to center 2" 30" radius

28" radius

3"

Cut along this line 26" radius

4"

24" radius

5"

O" 1" 2" 3" 4" 5" 6" 7" 8" 9" 1O" 11" 12" 13" 14" 15" 16" 17" 18" 19" 2O" 21" Tangent extension line 60" 50" TS radius radius TX 0" SC locations TEMPLATE B for various radii For approach to curves 40" radius from 20" to 60 " radius Circle finder 36" radius 50" to center 60" to center 40" to center 36" to center points P 30" to center 27.5" to center

30" radius 25" to center 1" 22" to center

27.5" radius 20" to center

25" radius 2"

Cut along this line

22" radius

3"

20" radius These templates are produced at 50 4" percent on legal size paper. To create O" 1" 2" 3" 4" 5" 6" 7" 8" 9" 1O" 11" 12" 13" 14" 15" 16" 17"

36" 48" Tangent extension line radius radius 32" 40" proper scale, print at 200 percent. radius radius TS TX 0" SC locations TEMPLATE C for various radii For approach to curves

28" Circle finder radius from 16" to 48 " radius points P 36" to center 32" to center Grid scale is marked on each template. 48" to center 40" to center 24" radius 28" to center

22" radius 24" to center 1" 22" to center

20" to center Center line of track on spiral 18" to center

20" radius 16" to center

18" radius

2"

16" radius Cut along this line 3" O" 1" 2" 3" 4" 5" 6" 7" 8" 9" 1O" 11" 12" 13" 14" Tangent extension line 42" 36" radius radius 28" TS radius TX 0" TEMPLATE D For approach to curves

24" Circle radius from 14" to 42" radius finder 21" radius SC locations

42" to center points P for various radii 36" to center 28" to center

24" to center Center line of track on spiral 21" to center 1" 18" radius 18" to center 16" to center 14" to center

16" radius

2"

14" radius

Cut along this line

O" 1" 2" 3" 4" 5" 6" 7" 8" 9" 1O" 11" 12" Tangent extension line 32" radius 36" 30" 21" radius radius 24" TS radius radius TX 0" TEMPLATE E For approach to curves from 12" to 36" radius 18" radius Circle finder 17" radius SC locations points P 16" radius for various radii 36" to center 33" to center 30" to center 24" to center 21" to center Center line of track on spiral 18" to center

17" to center 16" to center 15" radius 15" to center 1" 14" to center 13" to center

14" radius 12" to center

Cut along this line 13" radius

2" 12" radius

O" 1" 2" 3" 4" 5" 6" 7" 8" 9" 1O"

30" radius 20" 25" 18" TS radius radius radius TX 0" SC locations TEMPLATE F Tangent extension line for various radii For approach

15" radius to curves from Circle finder 10" to 30" radius points P 12.5" radius 30" to center 20" to center 25" to center 18" to center 15" to center 1" 12.5" to center 10" to center 11" to center 11"

Center line of track on spiral 11" radius

Cut along this line 10" radius

O" 1" 2" 3" 4" 5" 6" 7" 8" Tangent extension line 24" radius 20" radius 16" 14" 18" radius These templates are produced at 50 TS radius radius TX 0" TEMPLATE G For approach 12" percent on letter-size paper. To create radius 11" radius 10" to curves from Circle finder radius 8" to 24" 9" radius proper scale, print at 200 percent. points P SC locations radius 24" to center 20" to center 18" to center 16" to center 14" to center for various radii 12" to center 11" to center 11" 10" to center 9" to center 1" 8" to center Center line of track on spiral 8" radius Grid scale is marked on each template. Cut along this line